Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+8y &= 7 \\ 2x+3y &= -7\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -3y-7$ Divide both sides by $2$ to isolate $x$ $x = {-\dfrac{3}{2}y - \dfrac{7}{2}}$ Substitute this expression for $x$ in the first equation. $-2({-\dfrac{3}{2}y - \dfrac{7}{2}}) + 8y = 7$ $3y + 7 + 8y = 7$ Simplify by combining terms, then solve for $y$ $11y + 7 = 7$ $11y = 0$ $y = 0$ Substitute $0$ for $y$ in the top equation. $-2x+8( 0) = 7$ $-2x = 7$ $-2x = 7$ $x = -\dfrac{7}{2}$ The solution is $\enspace x = -\dfrac{7}{2}, \enspace y = 0$.